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Math Expert V
Joined: 02 Sep 2009
Posts: 61544
If x < 0, is y/x < 1 ? (1) y < x (2) y < 0  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 71% (01:15) correct 29% (01:01) wrong based on 21 sessions

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If $$x < 0$$, is $$\frac{y}{x} < 1$$ ?

(1) $$y < x$$

(2) $$y < 0$$

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GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4359
Re: If x < 0, is y/x < 1 ? (1) y < x (2) y < 0  [#permalink]

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Top Contributor
Bunuel wrote:
If $$x < 0$$, is $$\frac{y}{x} < 1$$ ?

(1) $$y < x$$

(2) $$y < 0$$

Target question: Is $$\frac{y}{x} < 1$$ ?
This is a good candidate for rephrasing the target question.

Since x is NEGATIVE, we can take: $$\frac{y}{x} < 1$$...
...and multiply both sides by x to get: $$y > x$$ [aside: since we multiplied both sides of an inequality by a negative value, we reverse the direction of the inequality symbol]

REPHRASED target question: Is $$y > x$$ ?
Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

Once we've rephrased the target question, we can easily deal with the two statements

Statement 1: $$y < x$$
So, the answer to the REPHRASED target question is NO, y is NOT greater than x
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: $$y < 0$$
So we now know that x and y are both negative.
This is not enough information to answer the REPHRASED target question. Here are two possible cases:
Case a: x = -1 and y = -2. In this case, the answer to the REPHRASED target question is NO, y is NOT greater than x
Case b: x = -2 and y = -1. In this case, the answer to the REPHRASED target question is YES, y IS greater than x
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
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GMAT Club Legend  V
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Location: India
Concentration: Sustainability, Marketing
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Re: If x < 0, is y/x < 1 ? (1) y < x (2) y < 0  [#permalink]

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given
x<0
x is -ve
and find y/x<1
#1
y<x
so if x = -1 , y =-2
so y/x<1 ; no
sufficient
#2
y<0
in that case y=x is possible so we get both yes and no for y/x<1
Insufficient
IMO A

Bunuel wrote:
If $$x < 0$$, is $$\frac{y}{x} < 1$$ ?

(1) $$y < x$$

(2) $$y < 0$$ Re: If x < 0, is y/x < 1 ? (1) y < x (2) y < 0   [#permalink] 14 Jan 2020, 08:08
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